spectrum is treated as a continuous function. If the spectrum 
were discrete jumps in E,(,0) as in equations (9.38b) and (9.39), 
this step would not be needed. 
['(#,0) could be called the distortion correction function. 
It is the Jacobian or equation (12.34) and it corrects for the 
squeezing together of (12.36) when it is changed to (12.37). 
Consider an example to clarify this point. Suppose that (12.36) 
is given by a constant value from # equal to 27/10 toH equal to 
2r/9 and for en equal to -1/30 to +1r/30 and by zero otherwise, and 
that (12.37) is the same except that 0, ranges from -7/60 to +1/60. 
Both (12.36) and (12.37) represent the average potential energy at the 
new point of observation, and yet the integral over # and 6p" for 
the first case is not equal to the integral over M and Op in the 
second case. But the value of 06,*/de, in this case is equal to 
two radians per radian, and thus doubling the value of the second 
spectrum corrects the value of the average potential energy. 
The power spectrum of the waves in the vicinity of the point 
under study in the transition zone is now known. It is given by 
equation (12.38). In terms of the XpoVR coordinate system at the 
point, C, in figure 32, and in terms of the p 99p» power spectrum 
defined there by the above procedures, the short crested sea surface 
near Xp and YR equal to zero is given by equation (12.39). In appear-= 
ance, the sea surface will be different in many ways from the sea sur- 
face at the point, B. The procedures described above predict many 
properties of the waves at the point C which are verifiable by 
aerial photographs and observational procedures. The properties 
will be described later. 
One property which follows from the derivation is given by 
a 
